[Math] Finding X and Y coordinates from two angles

trigonometry

I have a triangle ABC in the x-y coordinate plane.

Corners A and B lie on x-axis. Length of AB is known. Angles A and B are also known.

Question: Find (x,y) coordinates of corner C.

Best Answer

Another possibility is as follows: this solution to your problem involves using the fact that the slope of a line making an angle $\theta$ with the positive x-axis is $\tan\;\theta$; now, what you have are two lines with slopes $\tan\;A$ and $\tan(\pi-B)$ in one case, and slopes $\tan\;B$ and $\tan(\pi-A)$ in the other. Construct the point-slope form for the two lines through $A$ and $B$, and find their intersection through the usual methods.

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